Electric field of a plane electromagnetic wave propagating through a non-magnetic medium is given by $E=20 \cos \left(2 \times 10^{10} t-200 x\right) V / m$. The dielectric constant of the medium is equal to: (Take $\mu_{\mathrm{r}}=1$)

JEE Main · 2021 · 01 Sep 2021 · Shift 2 · EM Waves

Electric field of a plane electromagnetic wave propagating through a non-magnetic medium is given by

E = 20 cos (2 \times 1 0^{10} t - 200 x) V / m

. The dielectric constant of the medium is equal to: (Take

μ_{r} = 1

)

(A) $\frac{1}{3}$
(B)3
(C)2
(D)9✓ Correct

Answer: (D)

Solution

Comparing

E = 20 cos (2 \times 1 0^{10} t - 200 x)

with

E_{0} cos (ω t - k x)

gives

ω = 2 \times 1 0^{10} rad/s

and

k = 200 m^{- 1}

, so the phase speed is

v = \frac{ω}{k} = 1 0^{8} m/s

. The refractive index is

n = \frac{c}{v} = \frac{3 \times 1 0 ^{8}}{1 0 ^{8}} = 3

. Since

n = ε_{r} μ_{r}

with

μ_{r} = 1

, the dielectric constant is

ε_{r} = n^{2} = 9

JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Single correct option

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